MATLAB: Big M constraints bringing an infeasinle solution

big m constraintsmilp problemOptimization Toolbox

Here Tins is a decision variable of size=(24,1) in my optimization problem. The value of Tins(min_des) =20 while value of Tins(max_des) = 23.

I have tried using the following constraints for the above equation in MILP problem.

(Tmin – Tins) – M1*(1-BCac) <= 0 where M1 is an upper bound on (Tmin – Tins)

(Tins – Tmax) – M2*BCac <= 0 where M2 is an upper bound on (Tins – Tmax)

But if its supposed that Tins=27

then my first constraint gets satisfied with both BCac=1 and BCac=0

although the second constraint is satisfied at BCac=1 only, which is correct.

But due to the first constraint, my program is getting an infeasible solution.

Any help would be deeply appreciated.

Best Answer

Thanks a lot Mam, I too figured it out that solve options is introduced recently in the 2018a version of Matlab. I was giving out of bounds initial value to the Tins variable. Moreover, one of the big M constraint in my main program was given a wrong form. Also there were two equality constraints of Tins variable(both containing its formula for cooling and heating version), I edited that formula and now my program is giving satisfactory results.

Thanks a lot to Matt J for helping me out.

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The issue is with

Psofc=((hLHV*h2.*b1)+(gLHV*GgSOF.*b2))*sofeff;

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When you use intlinprog, even the constraints must be linear.

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The if-constraints (logical constraints, implication constraints) can be modeled with linear constraints and binary variables.

To see how to do this, suppose you have a binary variable y that should be 1 when x > 0. The constraint x - M*y <= 0, where M is an upper bound on x, will enforce this. When x > 0, y must be 1; the only other possible value for y is 0 and if y were 0, the constraint reduces to x <= 0, a contradiction.

To formulate constraint (6), make two constraints

(Tmin - Tins) - M1*(1-BCac) <= 0 where M1 is an upper bound on (Tmin - Tins)
(Tins - Tmax) - M2*BCac <= 0 where M2 is an upper bound on (Tins - Tmax)

The resulting constraints are called big-M constraints or indicator constraints. The y variable is called an indicator variable.

Best Answer

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